New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory
In this paper, we study the following quasilinear Schrödinger equation \begin{equation*} \begin{split} -\Delta u&+V(x)u-\kappa u\Delta(u^2)+\mu\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\\ &+\mu\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s)\text{d}s\right)u=f(u)\quad\text{in}~\mat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9074 |
| _version_ | 1827951129958285312 |
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| author | Yingying Xiao Chuanxi Zhu |
| author_facet | Yingying Xiao Chuanxi Zhu |
| author_sort | Yingying Xiao |
| collection | DOAJ |
| description | In this paper, we study the following quasilinear Schrödinger equation
\begin{equation*}
\begin{split}
-\Delta u&+V(x)u-\kappa u\Delta(u^2)+\mu\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\\
&+\mu\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s)\text{d}s\right)u=f(u)\quad\text{in}~\mathbb{R}^2,
\end{split}
\end{equation*}
where $\kappa>0$, $\mu>0$, $V \in \mathcal{C}^1(\mathbb{R}^2,\mathbb{R})$ and $f \in \mathcal{C}(\mathbb{R},\mathbb{R})$. By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions. |
| first_indexed | 2024-04-09T13:36:58Z |
| format | Article |
| id | doaj.art-1fc7d6d52880477086ee73175a147646 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:58Z |
| publishDate | 2021-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1fc7d6d52880477086ee73175a1476462023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-09-0120217311710.14232/ejqtde.2021.1.739074New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theoryYingying Xiao0Chuanxi Zhu1Nanchang University, Nanchang, Jiangxi, P. R. ChinaNanchang University, Nanchang, Jiangxi, P. R. ChinaIn this paper, we study the following quasilinear Schrödinger equation \begin{equation*} \begin{split} -\Delta u&+V(x)u-\kappa u\Delta(u^2)+\mu\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\\ &+\mu\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s)\text{d}s\right)u=f(u)\quad\text{in}~\mathbb{R}^2, \end{split} \end{equation*} where $\kappa>0$, $\mu>0$, $V \in \mathcal{C}^1(\mathbb{R}^2,\mathbb{R})$ and $f \in \mathcal{C}(\mathbb{R},\mathbb{R})$. By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9074gauged schrödinger equationpohožaev identityground state solutions |
| spellingShingle | Yingying Xiao Chuanxi Zhu New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory Electronic Journal of Qualitative Theory of Differential Equations gauged schrödinger equation pohožaev identity ground state solutions |
| title | New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory |
| title_full | New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory |
| title_fullStr | New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory |
| title_full_unstemmed | New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory |
| title_short | New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory |
| title_sort | new results on the existence of ground state solutions for generalized quasilinear schrodinger equations coupled with the chern simons gauge theory |
| topic | gauged schrödinger equation pohožaev identity ground state solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9074 |
| work_keys_str_mv | AT yingyingxiao newresultsontheexistenceofgroundstatesolutionsforgeneralizedquasilinearschrodingerequationscoupledwiththechernsimonsgaugetheory AT chuanxizhu newresultsontheexistenceofgroundstatesolutionsforgeneralizedquasilinearschrodingerequationscoupledwiththechernsimonsgaugetheory |